Bayesian logical data analysis for the physical sciences a comparative approach with Mathematica support

Preface Acknowledgements 1. Role of probability theory in science 2. Probability theory as extended logic 3. The how-to of Bayesian inference 4. Assigning probabilities 5. Frequentist statistical inference 6. What is a statistic? 7. Frequentist hypothesis testing 8. Maximum entropy probabilities 9. Bayesian inference (Gaussian errors) 10. Linear model fitting (Gaussian errors) 11. Nonlinear model fitting 12. Markov Chain Monte Carlo 13. Bayesian spectral analysis 14. Bayesian inference (Poisson sampling) Appendix A. Singular value decomposition Appendix B. Discrete Fourier transforms Appendix C. Difference in two samples Appendix D. Poisson ON/OFF details Appendix E. Multivariate Gaussian from maximum entropy References Index.